Defining parameters
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 14 | 46 |
Cusp forms | 36 | 10 | 26 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
320.2.c.a | $2$ | $2.555$ | \(\Q(\sqrt{-1}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots\) |
320.2.c.b | $2$ | $2.555$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots\) |
320.2.c.c | $2$ | $2.555$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots\) |
320.2.c.d | $4$ | $2.555$ | \(\Q(i, \sqrt{5})\) | \(\Q(\sqrt{-5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)